What is the centroid of a polygon?

The centroid is the arithmetic mean position of all points in the polygon — the geometric center of mass, assuming uniform density. It is the point where a flat cardboard cutout of the shape would balance perfectly.

What formula does this use?

It uses the standard centroid formula for simple polygons: Cx = (1/6A) × Σ(xᵢ + xᵢ₊₁)(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ) and the analogous formula for Cy, where A is the signed area from the Shoelace formula.

Does the polygon need to be closed?

No. The tool automatically closes the polygon by connecting the last vertex back to the first before computing.

Does vertex order (clockwise vs. counter-clockwise) matter?

No. The formula uses the absolute value of the signed area, so the centroid is the same regardless of whether vertices are listed clockwise or counter-clockwise.

Does this work for geographic (lat/lon) coordinates?

Yes, for small regions. Treat latitude as y and longitude as x. The result gives the centroid in degrees. For large regions spanning many degrees, a spherical centroid formula would be more accurate.

What if my polygon is self-intersecting?

The formula is only correct for simple (non-self-intersecting) polygons. Self-intersecting polygons will produce a mathematically defined but geometrically misleading centroid.

Centroid of Polygon Calculator

Name: Centroid of Polygon Calculator
Availability: InStock
Author: Nham Vu

Enter polygon vertex coordinates and instantly get the geometric centroid (cx, cy) using the exact signed-area formula.

Vertex Coordinates

One vertex per line — "x, y"

Result

Enter coordinates and press Calculate

Polygon Preview

Preview updates after calculating

Summary

Enter polygon vertex coordinates and instantly get the geometric centroid (cx, cy) using the exact signed-area formula.

How it works

Enter one vertex per line in the format "x, y" (at least 3 vertices required).
The tool parses each pair and builds an ordered vertex list.
The signed area is computed using the Shoelace formula.
The centroid x and y coordinates are derived from the standard weighted-sum formula over consecutive edge pairs.
Results are displayed with 6 decimal places, and the polygon with its centroid is drawn on a canvas.

Use cases

Find the geographic center of a land parcel or survey polygon.
Compute the balance point of a flat shape in engineering or physics.
Determine where to place a label or marker at the true center of a map region.
Verify GIS centroid calculations done in desktop software.
Calculate the center of a building footprint from corner coordinates.
Find the center of a sports field or zone polygon.

Frequently Asked Questions

Last updated: 2026-06-24 · Reviewed by Nham Vu